MODELING OF THERMAL JOINT RESISTANCE OF POLYMER METAL ROUGH INTERFACES

Transcription

1 MODELING OF THEMAL JOINT ESISTANCE OF POLYME METAL OUGH INTEFACES Majid Bahrami M. M. Yovanovich E. E. Marotta Department of Mechanical Engineering University of Waterloo Ontario, Canada Department of Mechanical Engineering Texas A&M University College Station, Texas, U.S.A IMECE 004, Nov. 3-9, 004, Anaheim, California, USA.

2 OVEVIEW Motivations and Objectives Problem Statement Thermal esistance of Microcontacts Deformation Mode of Asperities Present Model Comparison with Experimental Data Conclusions IMECE 004, Nov. 3-9, 004, Anaheim, California, USA.

3 MOTIVATIONS AND OBJECTIVES polymers are being used in many engineering applications most of Thermal Interstitial Materials (TIM) used in microelectronic cooling are polymers filled with conductive particles only a few studies, mostly experimental, exist in the literature develop a compact model for predicting the TC of polymer-metal interface in a vacuum IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 3

4 POBLEM STATEMENT only conduction through microcontacts contact resistance interface s b s << polymer bulk resistance s T contact resistance interface (thermal paste) heat source temperature profile T polymer solid solid heat sink z Q s Q k p Q k F F vacuum b L t r k contact resistance, constriction/spreading resistance of microcontacts thermal paste + j s b b t A k a p IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 4

5 CONFOMING OUGH JOINTS assumptions Gaussian roughness, isotropic surfaces are conforming σ σ m ω z m z mean plane Y σ mean plane ω smooth flat m Y equivalent rough z plane microcontacts do not interfere a) section through two contacting surfaces b) corresponding section through equivalent rough - smooth flat only normal forces deformation mechanics is determined only by equivalent rough surface σ σ + σ m m + m IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 5

6 PLASTIC AND ELASTIC MODELS plastic model: Cooper, Mikic, Yovanovich (969) elastic model: Mikic (974) assumed / / A elastic A plastic proposed an effective elastic microhardness H e H e E E m where υ υ + E E a priori assumption of deformation mode could lead to physically impossible effective elastic microhardness values H e > H mic impossible IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 6

7 DEFOMATION MODE OF ASPEITIES plasticity index introduced by Mikic (974) Polymer E GPa H mic GPa γ H mic γ E' m υ E' E υ + E γ γ 3.0 γ 3.0 plastic transition elastic ABS Delrin Nylon Phenolic Polycarbonate Polyethylene Polypropylene PVC Teflon Mikic concluded, as Greenwood and Williamson did, that the mode of deformation is not sensitive to applied load almost all polymer asperities deform plastically IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 7

8 PESENT MODEL surface asperities have Gaussian distribution equivalent rough surface approximation was used microcontacts deform plastically microhardness was measured for polymers studied microcontacts constriction/spreading and polymer bulk resistances are assumed to be in series Bahrami et al. [7] plastic model was used j s ( σ / m) t ( P / E ) p 0.565H mic 0 + k PA k a p A a joint temperatures are less than polymer glass temperatures IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 8

9 COMPAISON WITH DATA 0 Delrin 0 s presentmodel j s b j present model j b j Delrin j K/W 0 bulk resistance b contact resistance s P kpa j K/W 0 bulk resistance b contact resistance s P kpa IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 9

10 COMPAISON WITH DATA j K/W 0 Polyethylene s b j 0 present model j contact resistance s bulk resistance b j K/W 0 PVC s b j 0 bulk resistance b present model j contact resistance s P kpa P kpa IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 0

11 IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. NON-DIMENSINAL PAAMETE a non-dimensional parameter is proposed based on non-dimensional parameter ( ) ( ) mic s p p b s b j j H P P k k k E P t P m k / / / / * * 0 * * * Θ + Θ σ Θ >> Θ Θ << j s s b j b controls important, controls

12 COMPAISAON WITH EXPEIMENTAL DATA j / b 0 7 data points Model relative MS difference between model and data.7% 0 present model j / b s / b Delrin, FM Delrin, FM Poly, FM PVC, FM Delrin Polycarbonate Polyethylene Teflon ABS Polypropylene PVC 0 0 bulk resistance asymptote s / b TC asymptote FM: Fuller and Marotta 00 data P/H mic IMECE 004, Nov. 3-9, 004, Anaheim, California, USA.

13 SUMMAY AND CONCLUSIONS it is shown that the deformation mode of asperities is plastic in most of polymers studied a compact model is developed that assumes plastic deformation in asperities comparison of the present model with experimental data shows good agreement a non-dimensional parameter is introduced that specifies the significance of the microcontacts constriction/spreading resistance over the polymer layer bulk resistance IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 3

14 ACKNOWLEDGMENTS Natural Sciences and Engineering esearch Council of Canada (NSEC) The Center for Microelectronics Assembly and Packaging (CMAP) IMECE 004, Nov. 3-9, 004, Anaheim, California, USA. 4